Accommodation options in Nairobi generally fall in two camps: the really expensive and the cheap and nasty.
Ole Dume isn't that expensive, especially if you negotiate a deal for a stay of a few days or more. You can knock it down to around 50 to 75 dollars per night depending on your length of stay. We stayed here for four weeks and got a cracking deal. It's got great rooms (but avoid the ones on the top floor at all cost) which are large, light and very clean.
Our one bed apartment had a kitchen, living room, balcony, bedroom and bathroom. I think they have two and three bedders too. There was a TV and wifi (generally ok for email but not the best). There's a pool and a decent onsite restaurant which does a good veg curry. They'll do room service too.
Probably the best thing is the staff who are always very helpful. I was selling a car at the time and they didn't mind the people coming and going to look at the vehicle.
Decent location too.